Question: Explain why pipes burst in cold weather.Answer: People who have not studied acoustics think that Thor bursts the pipes, but we know that is nothing of the kind for Professor Tyndall has burst the mythologies and has taught us that it is the natural behaviour of water (and bismuth) without which all fish would die and the earth be held in an iron grip. (1881)

Genuine student answer* to an Acoustics, Light and Heat paper (1881), Science and Art Department, South Kensington, London, collected by Prof. Oliver Lodge. Quoted in Henry B. Wheatley, Literary Blunders (1893), 186-7, Question 10. (*From a collection in which Answers are not given verbatim et literatim, and some instances may combine several students' blunders.) Webmaster notes that “fish would die” may refer to being taught that water's greatest density is at 4°C, and sinks below a frozen surface, so bodies of water can remain liquid underneath, to the benefit of the fish. The student was likely taught that bismuth, like water, expands when it freezes.

Faraday, who had no narrow views in regard to education, deplored the future of our youth in the competition of the world, because, as he said with sadness, “our school-boys, when they come out of school, are ignorant of their ignorance at the end of all that education.”

In Inaugural Presidential Address (9 Sep 1885) to the British Association for the Advancement of Science, Aberdeen, Scotland, 'Relations of Science to the Public Weal', Report to the Fifty-Fifth Meeting of the British Association (1886), 11.

I should rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.

From Presidential Address (1869) to the British Association, Exeter, Section A, collected in Collected Mathematical Papers of Lames Joseph Sylvester (1908), Vol. 2, 657. Also in George Edward Martin, The Foundations of Geometry and the Non-Euclidean Plane (1982), 93. [Note: “plummet sound” refers to ocean depth measurement (sound) from a ship using a line dropped with a weight (plummet). —Webmaster]

J. J. Sylvester was an enthusiastic supporter of reform [in the teaching of geometry]. The difference in attitude on this question between the two foremost British mathematicians, J. J. Sylvester, the algebraist, and Arthur Cayley, the algebraist and geometer, was grotesque. Sylvester wished to bury Euclid “deeper than e’er plummet sounded” out of the schoolboy’s reach; Cayley, an ardent admirer of Euclid, desired the retention of Simson’s Euclid. When reminded that this treatise was a mixture of Euclid and Simson, Cayley suggested striking out Simson’s additions and keeping strictly to the original treatise.

The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.

The mathematics of the twenty-first century may be very different from our own; perhaps the schoolboy will begin algebra with the theory of substitution groups, as he might now but for inherited habits.

From Address before the New York Mathematical Society, Bulletin of the New York Mathematical Society (1893), 3, 107. As cited in G.A. Miller, 'Appreciative Remarks on the Theory of Groups', The American Mathematical Monthly (1903), 10, No. 4, 89.
https://books.google.com/books?id=hkM0AQAAMAAJ
1903

The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life. What would we not give to make it possible for us to steal a look at a book that will serve primary schools in a hundred years?

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan